Using the following data, calculate the mean absolute deviation: 7 2 8 5 9 9 5 6 8 1 What is the mean absolute deviation for these data? (4 points) A. 2.2 B. 6 C. 6.5 D. 8

Question

asked Dec 25, 2019 180k views

2 Answers

Vcampitelli · Answer 1 · 2019-12-29T17:24:26+0000

Answer:

Option A - 2.2

Explanation:

Given : Data 7, 2, 8, 5, 9, 9, 5, 6, 8, 1.

To find : What is the mean absolute deviation for these data?

Solution :

Step 1 - Calculate the mean of the data,

$M=(\sum x_n)/(n)$

M=(7+2+8+5+9 +9+5+6+8+1)/(10)

M=(60)/(10)

M=6

The mean is 6.

Step 2 - Calculate the distance between each data point and the mean.

Data points Distance from mean

7 |7-6| = 1

2 |2-6| = 4

8 |8-6| = 2

5 |5-6| = 1

9 |9-6| = 3

5 |5-6| = 1

6 |6-6| = 0

8 |8-6| = 2

1 |1-6| = 5

Step 3 - Add all the terms of distance from mean

X=1+4+2+1+3+3+1+0+2+5=22

Step 4 - Apply mean absolute deviation formula,

$MAD=(\sum X)/(n)$

MAD=(22)/(10)

MAD=2.2

Therefore, Option A is correct.

The mean absolute deviation is 2.2.